cp's OEIS Frontend

A254658 Numbers of words on alphabet {0,1,...,7} with no subwords ii, where i is from {0,1,2,3}.

%I A254658 #24 Jan 21 2023 13:40:29
%S A254658 1,8,60,452,3404,25636,193068,1454020,10950412,82468964,621084396,
%T A254658 4677466628,35226603980,265296094372,1997979076524,15047037913156,
%U A254658 113321181698188,853436423539940,6427339691572332,48405123535166084,364545223512451916,2745437058727827748
%N A254658 Numbers of words on alphabet {0,1,...,7} with no subwords ii, where i is from {0,1,2,3}.
%C A254658 a(n) equals the number of octonary sequences of length n such that no two consecutive terms differ by 6. - _David Nacin_, May 31 2017
%H A254658 Colin Barker, <a href="/A254658/b254658.txt">Table of n, a(n) for n = 0..1000</a>
%H A254658 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,4).
%F A254658 G.f.: (1 + x)/(1 - 7*x -4*x^2).
%F A254658 a(n) = 7*a(n-1) + 4*a(n-2) with n>1, a(0) = 1, a(1) = 8.
%F A254658 a(n) = (2^(-1-n)*((7-sqrt(65))^n*(-9+sqrt(65)) + (7+sqrt(65))^n*(9+sqrt(65)))) / sqrt(65). - _Colin Barker_, Jan 21 2017
%t A254658 RecurrenceTable[{a[0] == 1, a[1] == 8, a[n] == 7 a[n - 1] + 4 a[n - 2]}, a[n], {n, 0, 20}]
%t A254658 LinearRecurrence[{7,4},{1,8},30] (* _Harvey P. Dale_, Jan 21 2023 *)
%o A254658 (Magma) [n le 1 select 8^n else 7*Self(n)+4*Self(n-1): n in [0..20]];
%o A254658 (PARI) Vec((1 + x) / (1 - 7*x -4*x^2) + O(x^30)) \\ _Colin Barker_, Jan 21 2017
%Y A254658 Cf. A015561, A055099, A126473, A126501,  A126528, A254598, A254602.
%K A254658 nonn,easy
%O A254658 0,2
%A A254658 _Milan Janjic_, Feb 04 2015